(SPOILERS) Bluebell, Jessie, and Pincher all are relatively minor characters in the book, and in the last chapter it is mentioned that they have died. We never learn how, and the mention is brief.
(POSSIBLE SPOILERS) Mr Jones abuses alcohol, though it really is only talked about in the first and maybe second chapters. The pigs drink alcohol and get drunk.
(Spoiler) After overworking himself, Boxer the horse is sent to a glue factory under the guise that he'll be getting medical treatment. His actual death doesn't occur in-story, though.
(SPOILER) Yes. A goose who admits to betraying Napoleon kills himself by eating nightshade berries. It is only briefly mentioned, and it is never brought up again.
(SPOILER) Many of the chickens express concern over their eggs when Napoleon wants to sell them, though it is unclear if these eggs have been fertilized.